Categorical and Quantitative Variables

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Categorical and Quantitative Variables: meaning, method and solved example (AP Statistics) – Maths PDF

In short: Categorical and quantitative variables split all data into two types: categorical values sort individuals into labeled groups, and quantitative values record amounts where arithmetic means something.

AP StatisticsStatisticsAP Statistics Unit 1

What is Categorical and Quantitative Variables?

Every column in a data set is either one of the categorical and quantitative variables. A categorical variable answers “which group?”, such as favorite pizza topping or bus route. A quantitative variable answers “how much?” or “how many?”, such as minutes of homework or height in inches.

The test is simple: if averaging the values makes sense, the variable is quantitative. Zip codes, jersey numbers and phone area codes are written with digits, yet they only name groups, so they are categorical. The type decides which graphs and summaries are legitimate: bar charts and counts for categories, histograms and means for numbers.

How to spot it

  • A survey question offers choices such as yes or no, a brand, or a grade level, so the answers are labels.
  • The column holds measurements with units like minutes, dollars or pounds, and differences between values are meaningful.
  • You must pick a display, so you need to sort the data into categorical and quantitative variables first.
  • Numerals appear in the data but adding them would be nonsense, as with student ID numbers.

The method

  1. To separate categorical and quantitative variables, name the individuals in the data set and the variable measured on each one.
  2. Ask whether averaging two values would give a meaningful result; if yes, quantitative.
  3. If the values only sort individuals into groups, even when written as numbers, call it categorical.
  4. Choose the matching tools: counts, bar charts and relative frequencies for categorical data; dotplots, histograms, mean and standard deviation for quantitative data.
Categoricalfavorite toppingpepperonicheesemushroom18126Quantitativehomework hours per week048touching bars: numbers on a scaleseparate bars: groups
Categories get gaps between bars; numeric values get touching bars along a number line.

Categorical and Quantitative Variables: solved example

Problem

A robotics team in Dayton records, for each of its 24 members: grade level (9, 10, 11 or 12), number of competitions attended, favorite programming language, and the member’s jersey number. Classify each variable.

Solution

Grade level uses the numbers 9 to 12 only as labels for groups, and averaging grade levels says little, so it is categorical (some courses treat it as ordinal).

Competitions attended is a count where differences and means make sense: quantitative.

Favorite language is a label: categorical. The jersey number identifies a person, and a mean jersey of 17 has no meaning: categorical.

Try it

Question 1

Is a student’s zip code a categorical or a quantitative variable?

Show the answer

Categorical. Zip codes are numerals that name regions, and adding or averaging them produces nothing useful.

Question 2

Which graph suits “number of siblings” for 30 students: a bar chart of labels or a histogram or dotplot?

Show the answer

A dotplot or histogram, because the number of siblings is quantitative and sits on a number line.

Categorical and Quantitative Variables vs. Random Variable

Categorical and quantitative variables describe columns of observed data on real individuals. A random variable is different: it attaches a number to each outcome of a chance process, before anything is observed, together with a probability for every value. Data columns may hold labels; a random variable never does.

Random Variable

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